具连续时滞的三种群混合模型的周期正解

研究三种群之间既有捕食食关系又有竞争关系的混合非自治连续时滞模型，通过使用Burton定量和Lyapunov函数方法，得到了该系统存在唯一、全局渐近稳定周期正解的充分条件。     

时滞捕食者-食饵系统的稳定性

考虑一类带两个时滞项的捕食者——食饵系统的稳定性，利用比较方法得到系统局部渐近稳定的充分条件，放宽了已有文献对时滞项的限制。同时该方法可以推广到其多时滞和变系数，特别是周期系统，概周期系统的情形。     

一种PID型神经网络控制器

针对非线性的时滞系统 ,采用一种将PID控制规律融进神经元网络的控制器 ,并应用基于最小二乘递推算法的最小方差预测值来克服时滞误差 .运用Lyapunov稳定性定理 ,确定了系统稳定时控制器权系数的范围     

Transmission delay based control over networks with wireless links

To achieve the mobility of computers during communication, the TCP connections between fixed host and mobile host may often traverse wired and wireless networks, and the recovery of losses due to wireless transmission error is much different from congestion control. The paper analyzes the side effect of RTT estimation while making the TCP source to handle congestion and wireless error losses properly. Then present a strategy using information feedback by the last hop acknowledgement and monitoring the queuing level of the wired bottleneck link by calculating the changes in transmission delay along the path. With the identification of the early stage of congestion, it can respond to wired congestion quickly while keeping wireless link more reliable, and make TCP react to the different packets losses more appropriately. Foundation item: Supported by the National Natural Science Foundation of China (69874025) Biography: Zhou Zhi-zhao (1973-), male, Ph. D. candiate, research direction: data communication over heterogeneous networks.     

基于比率的三种群捕食系统的持久性与全局渐近稳定性

研究一类具有连续时滞和基于比率的两个捕食者和一个食饵的三种群系统，证明了该系统在适当条件下的一致持久性；通过构造Lyapunov泛函，给出了该系统在有时滞情况下的正平衡点全局渐近稳定的充分条件。     

带时滞反馈的非线性离散模型的性质

综合考虑描绘神经元动力性的非线性离散模型,得到了模型的2k m周期解及解的渐近性的充分条件.     

块隐式单步方法求解一类延迟微分代数方程

延迟微分代数方程(DDAEs)广泛应用于科学与工程各领域，但目前对这类问题的数值方法仅有很少量的研究．将块隐式单步方法应用于一类半显式指标1延迟微分代数方程，给出了方法的误差分析，理论分析和数值试验表明该方法对此类DDAEs的求解有良好的效果。     

Linear stability of numerical methods for systems of functional differential equations with a proportional delay

The numerical solution of functional differential equations with a proportional delay is considered. The stability of general linear methods for linear systems of neutral type is investigated. It is shown that a general linear method with strict stability at infinity can preserve the asymptotic stability of the underlying system if we employ an appropriate equi-stage interpolation to approximate the delay argument.     

中立型延迟微分方程Runge-Kutta方法的稳定性

研究以下中立型延迟微分方程y'(t)=Ly(t)+My(t-τ1)+Ny'(t-τ2) t≥0y(t)=g(t) t＜0其中L,M,N是d×d复矩阵,τ2≥τ1＞0,g(t)是给定的向量函数.证明了Runge-Kutta法是NGP-稳定的充分必要条件是它是A-稳定的.     

时滞B-BBM方程解的渐近性

研究了时滞B-BBM方程，利用Liapunov函数方法，证明了如果时滞参数充分小，该方程是指数稳定的，并给出了时滞参数关于初值和ε,β的精确估计．由此可以看出，当初值趋于无穷大或εβ→0时，时滞参数τ→0.